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arXiv · 0908.2671

Exel's crossed product for non-unital C*-algebras

Nathan Brownlowe·Iain Raeburn·Sean T. Vittadello
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Abstract

We consider a family of dynamical systems (A,alpha,L) in which alpha is an endomorphism of a C*-algebra A and L is a transfer operator for α. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show that the C*-algebra of a locally finite graph can be realised as one of these crossed products. When A is commutative, we find criteria for the simplicity of the crossed product, and analyse the ideal structure of the crossed product.

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Nathan Brownlowe, Iain Raeburn, Sean T. Vittadello. 2009-08-19. Exel's crossed product for non-unital C*-algebras. https://doi.org/10.1017/s030500411000037x

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